Analytical and statistical investigation on structural fluctuations induced radiation in photonic crystal slabs.

We extend the coupled-wave-theory (CWT) framework to a supercell lattice photonic crystal (PC) structure to model the radiation of high-Q resonances under structural fluctuations since they are inevitable in realistic devices. The comparison of CWT results and the finite-element-method (FEM) simulations confirm the validity of CWT. It is proved that the supercell model approaches a realistic finite-size PC device when the supercell size is large enough. The Q factors within fluctuated structures are constraint owing to the appearance of fractional orders of radiative waves, which are induced by structural fluctuations. For a large enough footprint size, the upper bound of the Q factor is determined by the fabrication precision, and further increasing the device size will no longer benefit the Q factor.